Spectral simulation and optimization of simulated parameters to fit experimental data are very powerful tools for data analysis in EPR spectroscopy. Recently Halpern and coworkers developed a fast algorithm for quantitation of inhomogeneously broadened EPR spectra (Voigt lineshape). They approximated the Voigt profile by a sum of Lorentzian and Gaussian functions and used the Levenberg-Marquardt algorithm for multidimensional optimization. We describe an even more accurate and flexible approach to linewidth simulation based on a fast convolution algorithm (FCA). FCA was also applied for calculating the partial derivative matrix required for Levenberg-Marquardt optimization. All fitting parameters, including dispersion contribution, and Lorentzian and Gaussian linewidths are extracted directly. A fixed hyperfine and/or superhyperfine pattern may be included in the fitting procedure without broadening of a CTPO EPR spectrum at various oxygen concentrations and to study the penetration of a 1.13 GHz microwave field into a lossy dielectric sample.